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A246918 The length of the shortest nontrivial integral cevian of an equilateral triangle of side n that divides an edge into two integral parts, or 0 if no such cevian exists. 4
0, 0, 7, 0, 7, 14, 13, 7, 21, 14, 31, 28, 43, 26, 13, 14, 73, 42, 91, 28, 19, 62, 133, 21, 35, 86, 63, 52, 211, 26, 241, 28, 37, 146, 31, 84, 343, 182, 49, 35, 421, 38, 463, 124, 39, 266, 553, 42, 91, 70, 79, 172, 703, 126, 49, 49, 97, 422, 871, 52, 931, 482 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
A cevian is a line segment which joins a vertex of a triangle with a point on the opposite side (or its extension).
A nontrivial cevian is one that does not coincide with a side of the triangle.
For an equilateral triangle of side n, the lengths of its cevians are the values of y in the solutions to x^2-y^2-n*x+n^2=0.
LINKS
Wikipedia, Cevian
PROG
(PARI)
\\ Returns the length of the shortest integral cevian of an equilateral triangle of side n.
shortest(n) = {
s=[];
m=12*n^2;
fordiv(m, f,
g=m\f;
if(f<=g && (f+g)%2==0,
x=(f+g)\2;
if(x%4==0,
s=concat(s, x\4)
)
)
);
s=Colrev(s)~;
if(#s==1, return(0));
for(i=1, #s, if(s[i]!=n, return(s[i])))
}
vector(100, n, shortest(n))
CROSSREFS
Sequence in context: A202996 A019597 A096444 * A055957 A165090 A341484
KEYWORD
nonn
AUTHOR
Colin Barker, Sep 07 2014
STATUS
approved

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Last modified May 28 19:55 EDT 2024. Contains 372919 sequences. (Running on oeis4.)